Question: Suppose you owe $500 on your credit card and you decide to make no new purchases and to make the…

Suppose you owe $500 on your credit card and you decide to make no new purchases and to make the minimum monthly payment on the account. Assuming that the interest rate on your card is 1% per month on the unpaid balance and that the minimum payment is 2% of the total (balance plus interest), your balance after \( t \) months is given by \( B(t) = 500(0.9898)^t \). Find your balance at each of the given times. Complete parts (a) through (e) below.

(a) six months

Solution

The problem asks you to find the balance on a credit card after a certain number of months using the formula \( B(t) = 500(0.9898)^t \). We will calculate the balance for different values of \( t \) as specified: (a) Find the balance after six months. First, identify the given values: - Initial balance: $500 - Formula: \( B(t) = 500(0.9898)^t \) - \( t = 6 \) Substitute \( t = 6 \) into the formula: \[ B(6) = 500(0.9898)^6 \] Calculate \( (0.9898)^6 \): \[ (0.9898)^6 \approx 0.9401 \] Multiply the results: \[ B(6) = 500 \times 0.9401 \approx 470.05 \] Therefore, the balance after six months is approximately $470.05.